I think it is not possible to change the restriction not prompted from the Web interface...at least for security reason.Could be a feature request: Add a flag on the restriction or on the report to allow value overwrite.

You may try to play with the Init Script of the report (but I am not sure it will work):Set your restriction as To be Prompted, and in the Init Script,change it to not prompted...may be it will work.

To edit the Init Script: Click on the root 'Views' node in the tree view and edit the related property.

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